Planimeter device



Nov. 19, 1963 H, WILEY 3,110,967

PLANIMETER DEVICE Filed April 12, 1962 2 Sheets-Sheet 1 INVEN I OR HighWiley ATTORNEYS Nov. 19, 1963 H. WILEY 3,110,967

PLANIMETER DEVICE Filed April 12, 1962 2 Sheets-Sheet 2 INVENTOR HughWiley BY fiwv/Mm ATTORNEYS United States Patent 0 3,116,967 LANlh ETEREEVECE Hugh Wiley, lill l Oxford t., Berkeley 7, Quilt. Filed Apr. 12,1962, Ser. No. 136,9il3 9 Claims. (til. 33-422.)

This invention relates to planimeters and partic larly to planimeters ofthe hatchet type. The invention involves novel planimeter features and anovel combination of planimeter and chart for directly reading the areaof the figure being measured.

A hatchet type planimeter is a well-known type of instrument andcomprises an elongated bar or frame having a pointed stylus at one endand a pursuit portion at the other end. The pursuit portion may be inthe form of a fixed hatchet edge lying in a plane containing the stylusor it may be an edge of a wheel or roller, the axis of which is sooriented that the plane of rotation includes the stylus. By thisarrangement the pursuit portion always follows or pursues the st ins anda. tangent to its path of travel always passes through the point of thestylus, wherever it may be at that instant. Throughout the presentspecification and claims, the term pursuing edge portion will beemployed to refer to either a fixed hatchet edge or a roller arrangementand the term hatchet type planimeter will refer to such an instrumenthaving either a fixed hatchet edge or one or more wheels or rollers.

In the conventional operation of such an instrument, the approximatecenter of gravity of the area to be measred is first located and a line,usually rectilinear, is drawn from that center of gravity to some pointin the periphery of the figure. The planimeter is then placed with thepoint of the stylus at the center of gravity of the figure and theposition of the contact point of the pursuing portion is marked orotherwise noted.

The stylus is then caused to trace along the line previously drawn tothe edge of the figure and is then caused to tram the outline of thefigure back to the starting point then again inwardly to the center ofgravity. The contact point of the pursuing portion will have beenlaterally displaced from its starting position, which new location isthen marked or noted. The displacement of the contact point is as if ithad been arcuately moved from its starting position to its finalposition about the cent-er of gravity of the figure as a pivot. The areaof the figure is the product of the distance from the stylus to thecontact point and the length of the are between the starting and finalpositions of the contact point.

The present invention involves novel features or" such a planimeterinstrument wherein means are provided for holding the stylusperpendicular to the figure at all times and ot thus render theinstrument highly stable and accurate. The invention also contemplatesthe combination of the hatchet type planimeter with a transparent sheetto be placed over the figure to be measured. The transparent sheet isprovided with means defining a starting point and an are upon which thecontact point or equivalent part of the pursuing portion rests when thepoint of the stylus is on the starting point. The are is graduateddirectly in terms of area, although it may be graduated in other factorswhich are directly proportional to area. in use, the transparent sheetis placed over the figure to be measured with the starting pointcoinciding approximately with the center of gravity of the figure. Theplanimeter is then placed on the sheet with its stylus at the startingpoint and the contact point of the pursuing portion at the zerograduation on the are. The figure is then traced in the mannerpreviously described and at the completion thereof the area of thefigure is read directly from the graduations along the arc. it is to beremembered that, at completion of the tracing, the contact point of thepurfit suing portion is again directly on the graduated arc. In certainforms of the invention, the contact point itself is not used as anindicating element, a separate pointer being provided which cooperateswith the graduated arc, thus rendering it easier to read the answersince the contact portion of a wheel or a hatchet edge at leastpartially obscures the graduations and renders an accurate readingthereof somewhat difficult.

It is, therefore, an object of this invention to provide a planirneterand chart combination whereby the area of an irregular figure may bemeasured without marking the figure or providing any marks on thesurface containing the figure.

Another object is to provide a novel planimeter structure especiallyadapted for use with the combination referred to.

Another object is to provide a planimeter and chart combination whereinthe chart can be calibrated to read directly in any values proportionalto the area of the figure.

A further object of the invention is to provide a planimeter and/or acombination as set forth that is simple and economical to construct yetreliable and accurate in operation.

Further and additional objects and advantages will become apparent tothose skilled in the art as the description proceeds with reference tothe accompanying drawings wherein;

FIG. 1 is a plan view of one form of planimeter in combination with anovel chart according to the present invention;

PEG. 2 is a side elevational view of the planimeter of FIG. 1;

PEG. 3 is a front view of the planimeter of PEG. 2, as viewed from theright hand side thereof;

FIG. 4 is a plan view, similar to PEG. 1, but showing a different formor" planimeter;

PEG. 5 is a side view of the panimeter of FIG. 4; and

FIG. 6 is a front end View of PEG. 5.

Referring first to FIG. 1, a sheet of paper or the like 2 is shownhaving delineated thereon an irregular outline 4, the area of which isto be measured. A fiat transparent sheet 6, which may be of plastic orthe like, is placed over the sheet 2 to overlie the FIG. 4. TLB Sheet 6is provided with a mark defining a starting position or point e fromwhich a straight line 9* extends. The point 8 and line 9 may be markedon the sheet s in any suitable manner. A circular are it is alsodelineated on the sheet 6 and is a circular are having its center at thepoint 8. As shown, the zero graduations on the are it are directly inline with the line 9 previously referred to, although the line 9 mayactually extend in any direction. As shown, the are 1% is graduated inunits of area, the outer side of the are being graduated in squareinches whereas the inside of the arc is graduated in units representingsquare centimeters. Also inscribed on the surface of the transparentsheet 6 is a light grid of lines 12 and 14 with the point 8substantially at the center thereof. The grid of lines 12 and 14 areprovided to make it easier to locate the approximate center of gravityof the irregular outline 4. By so placing the sheet 6 over the sheet 2that the number of squares bounded by the outline d is approximatelyequal in each or the four quadrants having point 3 as a center, then thepoint 3 will be at the approximate center of gravity of the figure.

The planim'eter comprises an elongated bar or frame 16 having a verticalpointed stylus 18 at its forward end. At its rearward end the frame orbar 16 is provided with a block 20 having a longitudinal slot 21 inwhich a sharpedged wheel 22 is journallcd on a pin 24. The wheel 22 andthe axis of pin 24 are so positioned that the plane defined by thesharpened periphery of the wheel contains 3 the point of the stylus l8and thus as the stylus 11% is moved to the right as seen in the figures,the wheel 22 will follow or pursue the stylus.

To operate the device the sheet 6 is placed over the outline 4 in thesame manner described, then the planimeter is placed over the assemblywith the point of stylus 18 on the starting point 8 of sheet 6 and withthe contact edge of wheel 22 lying directly on the zero graduation ofthe are it It is to be noted that the distance from the point of stylus13 to the contact point as of the wheel 22 is exactly equal to theradius of the arc til in this particular embodiment. After the parts areso positioned, the planimeter is manipulated to draw or trace along theline 9 with the point of stylus 13 until the stylus reaches theintersection of line and the outline 4. The stylus is then traced aroundthe outline 4 in a clockwise direction until the entire outline istraced back to the line d. The stylus is then moved along the line 9back to the starting point, at which time the planimeter will haveassumed an angularly displaced position as shown by dotted lines inFIG. 1. The point at which the wheel 22 rests on the arc ill nowindicates the number of units of area within the irregular outline 4.

As is apparent, the stylus 13 is mounted on a block or fitting 28carried by the rod 16 and which block is further provided with a bowedmetal member 3t preferably of somewhat springy characteristics. Themember 39 extends laterally of the bar 16 and downwardly so that itsouter ends lie approximately in a plane containing contact point 26, andthe point of stylus 18, and which plane is approximately perpendicularto the stylus 318. Thus, the spring arms 30 hold the stylus vertical atall times and insure maximum accuracy. Preferably, the spring armsnormally hold the point of stylus 13 just at or slightly above thesurface of sheet 6 to prevent gouging or scratching the sheet. As shownin FIGS. 2 and 3, the outermost ends of the spring arms 30 are dimpledor dished downwardly to define convex portions 32 to glide smoothly overthe transparent sheet 6.

While the description thus far has been with specific reference to aplanimeter having a rotatable sharpened wheel 22, it is to be understoodthat the combination described is of equal utility with a planimeterhaving a fixed hatchet edge providing a contact point 26, rather than arotatable wheel. Such planimeters are well-known in the art.

A second embodiment of the invention is shown in FIGS. 4 through 6 andwhich is employed in exactly the same manner as described in connectionwith P168. 1, 2 and 3 but wherein a diiferent form of planirneterstructure is utilized. The transparent sheet 6 may be substantiallyidentical in all respects to that described in connection with FIG. 1and the same reference numerals are used to designate correspondingportions. By briefly referring to FIG. 1 again, it will be noted thatthe only significant variable value determining the area of theirregular FlG. 4- is the angular displacement of the planimeter bar orframe 16 between its starting and final positions. Since the angularposition at the end of the tracing step is of a predetermined value, thegraduations or indications of area need not be exactly at the describedradius from point 8. In other words, the arc ltl shown in FIG. 1 couldbe at a substantially greater radius than that shown and a pointer orsimilar indicator could be attached to the planimeter to extendoutwardly to cooperate with the graduations of such arcuate scale, aslong as the graduations at the greater radius correspond exactly tothose at the radius described. In other words, graduations placed on anarc radially outwardly of the wheel 22 would still indicate the productof the distance from stylus 18 to contact point 26 and the length of thearc of displacement, which arc is at a radius equal to the distance fromstylus 18 to point 26.

With the above discussion in mind, the form shown in FIG. 4 will bereadily understandable. In this form of device, the planimeter comprisesa frame having a pair of longitudinal side members 36 joined at one endby a suitable fitting 33 which supports a pointed stylus 4th at theforward end of the frame. At the rearward end of the frame a spacer 42positions the outer ends of the members 35 and supports a fixed shaft 44on which a pair of laterally spaced wheels or rollers 46 are journalledfor independent free rotation. Preferably the peripheries of the wheelsare knurled or otherwise treated to provide non-slip characteristics. Inthis form of the invention, the arc it is positioned at a greater radiusfrom point 8 than the are described and shown in FIG. 1. It ispositioned outwardly far enough to be clear of the wheels so they do notobstruct a clear view of the graduations associated with the are. Apointer 48 is fixed on the spa er and extends downwardly and forwardlytherefrom (see FIG. 5) so that its point just touches the are 10 whenthe stylus is at the starting point 8. Thus, the final position of theplanirnetcr, after the outline has been traced, may be read directly atthe tip of the pointer 48 in terms of square inches, square centimeters,or other values directly proportional to area. Obviously, the pointerneed not be exactly centered on the frame of the planimeter but may beat any desired location laterally of that center as long as theoperation is started with the pointer at the zero graduation. It is tobe noted that the axis on which t. e wheels 4-6 rotate is perpendicularto the longitudinal axis of the planimeter frame so that the end of theframe carrying the wheels accurately follows or pursues the stylus 40.

While a limited number of specific embodiments of the invention havebeen shown and described herein, it is to be understood that the sameare merely illustrative and that other forms may be resorted to withinthe scope of the appended claims.

I claim:

1. In combination: a hatchet type planimeter having a tracing stylus anda pursuing portion in spaced and aligned relation to said stylus; and alight transmitting sheet of material raving means thereon defining astarting point, means on said sheet defining a circular arc having saidstarting point as its center, the radius of said are being substantiallyequal to the distance from said tracing stylus to said pursuing portion,graduations and indicia along said arc, said indicia defining valuesdirectly proportional to the length of said arc from a predeterminedzero position thereon, said pursuing portion including means cooperatingwith said graduations to indicate values thereof.

2. The combination defined in claim 1 including means on said sheetdefining a path extending from said starting point, in a directionradial to said arc.

3. The combination defined in claim 2 wherein said last-named meansdefines a straight-line path extending radial to said are and alignedwith said zero position thereon.

4. The combination defined in claim 1 wherein said indicia indicatevalues equal to the product of said length of said are and the distancefrom said starting point to said arc.

5. The combination defined in claim 1 including means fixed to saidplanimeter adjacent said stylus and having spaced portions slidablyengageable with said sheet on opposite sides of said stylus to hold saidstylus and edge portion in a substantially vertical plane. 7

6. The combination defined in claim 1 wherein said pursuing portioncomprises a pair of laterally spaced wheels and a pointer therebetweento constitute said means cooperating with said graduations.

'7. The combination defined in claim 6 wherein said pointer extends awayfrom said stylus, beyond the periphery of said wheels and terminates onsaid are when said istylus is at said starting point.

8. The combination defined in claim 1 including means on said sheetdefining a rectangular grid of lines covering a substantial areathereof, said starting point being substantially at the center of saidgrid.

9. The combination defined in claim 1 wherein said pursuing portioncomprises an arcuate contact member for engagement with said sheet; saidlast-named means comprising a pointer on said planirneter adjacent saicontact member.

References Cited in the file of this patent UNITED STATES PATENTSGoodman June 27, 1893 Chcllar Jan. 12, 1897 Dewitt et a1 Dec. 25, 1906Buvinger Apr.. 8, 1913 FOREIGN PATENTS Germany Feb. 23, 1895 France June27, 1952 Italy Mar. 24, 1950

1. IN COMBINATION: A HATCHET TYPE PLANIMETER HAVING A TRACING STYLUS ANDA PURSUING PORTION IN SPACED AND ALIGNED RELATION TO SAID STYLUS; AND ALIGHT TRANSMITTING SHEET OF MATERIAL HAVING MEANS THEREON DEFINING ASTARTING POINT, MEANS ON SAID SHEET DEFINING A CIRCULAR ARC HAVING SAIDSTARTING POINT AS ITS CENTER, THE RADIUS OF SAID ARC BEING SUBSTANTIALLYEQUAL TO THE DISTANCE FROM SAID TRACING STYLUS TO SAID PURSUING PORTION,GRADUATIONS AND INDICIA ALONG SAID ARC, SAID INDICIA DEFINING VALUESDIRECTLY PROPORTIONAL TO THE LENGTH OF SAID ARC FROM A PREDETERMINED